Convex fused lasso denoising with non-convex regularization and its use for pulse detection

Ankit Parekh, Ivan W. Selesnick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

25 Scopus citations

Abstract

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation. Originally, the 1 norm was used as a sparsity-inducing convex penalty function for the fused lasso signal approximation problem. However, the 1 norm underestimates signal values. Non-convex sparsity-inducing penalty functions better estimate signal values. In this paper, we show how to ensure the convexity of the fused lasso signal approximation problem with non-convex penalty functions. We further derive a computationally efficient algorithm using the majorization-minimization technique. We apply the proposed fused lasso method for the detection of pulses.

Original languageEnglish
Title of host publication2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509013500
DOIs
StatePublished - 11 Feb 2016
Externally publishedYes
EventIEEE Signal Processing in Medicine and Biology Symposium - Philadelphia, United States
Duration: 12 Dec 2015 → …

Publication series

Name2015 IEEE Signal Processing in Medicine and Biology Symposium - Proceedings

Conference

ConferenceIEEE Signal Processing in Medicine and Biology Symposium
Country/TerritoryUnited States
CityPhiladelphia
Period12/12/15 → …

Keywords

  • Sparse signal
  • fused lasso
  • non-convex regularization
  • pulse detection
  • total variation denoising

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